{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Introduction to Random Variables and Statistical Distributions" ] }, { "cell_type": "code", "execution_count": 113, "metadata": {}, "outputs": [], "source": [ "from scipy.stats import bernoulli, poisson, binom, norm, mvn\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "import matplotlib\n", "import pandas as pd\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "headimg = plt.imread('../data/quarterheads.jpg')\n", "tailimg = plt.imread('../data/quartertails.jpg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discrete random variables\n", "A discrete random variable can take a finite number of possible values. A toss of a two-sided coin can be thought of as a random variable, or a roll of a 6 sided dice. \n", "\n", "#### Probability distributions for discrete random variables\n", "A random variable is generated from a probability distribution. There are different types of distributions defined for discrete random variables. These include:\n", "- Bernoulli distribution\n", "- Binomial distribution\n", "- Multinoulli distribution\n", "- Poisson distribution\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Bernoulli distribution\n", "Bernoulli distribution represents a binary random variable which takes value 1 with success probability $p$ and value 0 with failure probability $q=1-p$. A bernoulli distribution has only one parameter: $p$." ] }, { "cell_type": "code", "execution_count": 180, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "theta = 0.5\n", "# let us draw a sample from a bernoulli distribution\n", "b = bernoulli.rvs(theta,size=1)\n", "print(b)\n", "if b[0] == 0:\n", " plt.imshow(tailimg)\n", " plt.axis('off')\n", "else:\n", " plt.imshow(headimg)\n", " plt.axis('off')\n", " " ] }, { "cell_type": "code", "execution_count": 183, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0\n", " 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1\n", " 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1\n", " 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1\n", " 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1\n", " 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0\n", " 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1\n", " 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0\n", " 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1]\n", "909\n" ] } ], "source": [ "# you can also draw samples simultaneously\n", "theta = 0.9\n", "samples = bernoulli.rvs(theta,size=1000)\n", "print(samples)\n", "# count the number of successes (sample = 1). What happens when you change p?\n", "print(np.count_nonzero(samples==1))" ] }, { "cell_type": "code", "execution_count": 185, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0.98, 'Bernoulli probability')" ] }, "execution_count": 185, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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A55L8W+CpwN5Wq9SPsN/21G8/ycxvUVYCq5j5Vfo7m/wwr7eWUC999/AqSs8FXtX0B9lvtZQM09I8qmo6yaXAjcws03RNVe1Ocknn+Gbg7cC1Sf6OmV9RXlZV9/StaD3s9dJvq+r2JDcAtwIPMrME2Vf7V7XU82cuwIuBv+j8ZkXqO8O0tICq2g5sn7Vvc9fr/cDz2q5LWshi/bazfSVwZZt1SYvpse9eC1zbXlXSwrwBUZIkSWrIMC1JkiQ1ZJiWJEmSGjJMS5IkSQ0ZpiVJkqSGDNOSJElSQ4ZpSZIkqSHDtCRJktSQYVqSJElqyDAtSZIkNWSYliRJkhoyTEuSJEkNGaYlSZKkhgzTkiRJUkOGaUmSJKkhw7QkSZLUkGFakiRJasgwLUmSJDVkmJYkSZIaMkxLkiRJDRmmJUmSpIYM05IkSVJDhmlJkiSpIcO0JEmS1JBhWpIkSWrIMC1JkiQ1ZJiWJEmSGjJMS5IkSQ0ZpiVJkqSGDNOSJElSQ4ZpSZIkqSHDtCRJktSQYVqSJElqyDAtSZIkNWSYliRJkhoyTEuSJEkNGaYlSZKkhloJ00nWJ7kjyZ4kl89x/DFJPpXkK0l2J3ltG3VJkiRJx2LZw3SSFcDVwIXAOuCiJOtmNXsjcFtVnQWcB/x+klXLXZskSZJ0LNoYmT4X2FNVe6vqILAV2DCrTQEnJgnwKOBbwHQLtUmSJEmNtRGmVwP7urYnO/u6XQU8HdgP/B3wpqp6cPaJkmxKsjPJzqmpqeWqV5IkSepJG2E6c+yrWdsXALcATwSeCVyV5NEP+aaqLVU1UVUTY2NjS1+pJEmSdBTaCNOTwKld2+PMjEB3ey3w8ZqxB/g68LQWapMW1MPNs29Jckvn66tJDiV5XD9qlSRJ7WsjTO8ATk+ytnNT4UZg26w2dwG/AJDk3wJPBfa2UJs0r15unq2qK6vqmVX1TODXgZuq6lvtVytJkvph5XL/gKqaTnIpcCOwArimqnYnuaRzfDPwduDaJH/HzLSQy6rqnuWuTVrEkZtnAZIcvnn2tnnaXwR8uKXaJEnSAFj2MA1QVduB7bP2be56vR94Xhu1SEdhrptnnzVXwySPBNYDl85zfBOwCWDNmjVLW6UkSeobn4Aoza+Xm2cP+yXgb+ab4uHNs5IkjSbDtDS/Xm6ePWwjTvGQJOlhxzAtza+Xm2dJ8hjgucAnW65PkiT1WStzpqVh1OPNswAvBv6iqu7rU6mSJKlPDNPSAha7ebazfS1wbXtVSdJoSrIe+ANmBjDeW1W/O0eb84B3AccB91TVc1stUprFMC1Jkvqua23/85m5Z2VHkm1VdVtXm8cC7wHWV9VdSR7fn2qlf+WcaUmSNAiOrO1fVQeBw2v7d3sFM09Mvgugqu5uuUbpIQzTkiRpEMy1tv/qWW3OAE5K8tkku5K8Zq4TJdmUZGeSnVNTU8tUrjTDMC1JkgZBL2v7rwTOBl4AXAD8ZpIzHvJNru2vFjlnWpIkDYJe1vafZOamw/uA+5LcDJwF3NlOidJDOTItSZIGQS9r+38S+NkkK5M8EngWcHvLdUo/wpFpSZLUd72s7V9Vtye5AbgVeJCZ5fO+2r+qJcO0JEkaED2u7X8lcGWbdUkLcZqHJEmS1JBhWpJGTJL1Se5IsifJ5XMcPy/Jd5Pc0vl6az/qlKRR4DQPSRohvTxFruNzVfWLrRcoSSPGkWlJGi29PEVOkrREDNOSNFp6eYocwHOSfCXJ9UmeMd/JfJKcJC3MMC1Jo6WXp8h9GXhSVZ0FvBu4br6T+SQ5SVqYYVqSRsuiT5Grqnur6vud19uB45Kc0l6JkjQ6DNOSNFoWfYpckickSef1ucz8XXCg9UolaQS4mockjZBeniIHvAz4lSTTwP3AxqqaPRVEktQDw7QkjZjFniJXVVcBV7VdlySNIqd5SJIkSQ0ZpiVJkqSGDNOSJElSQ4ZpSZIkqSHDtCRJktSQYVqSJElqyDAtSZIkNWSYliRJkhoyTEuSJEkNGaYlSZKkhgzTkiRJUkOGaUmSJKkhw7QkSZLUkGFakiRJasgwLUmSJDVkmJYkSZIaMkxLkiRJDRmmJUmSpIYM05IkSVJDhmlJkiSpIcO0JEmS1JBhWpIkSWrIMC1JkiQ1ZJiWJEmSGjJMS5IkSQ0ZpqUFJFmf5I4ke5JcPk+b85LckmR3kpvarlGSJPXPyn4XIA2qJCuAq4HzgUlgR5JtVXVbV5vHAu8B1lfVXUke359qJUlSPzgyLc3vXGBPVe2tqoPAVmDDrDavAD5eVXcBVNXdLdcoSZL6yDAtzW81sK9re7Kzr9sZwElJPptkV5LXzHWiJJuS7Eyyc2pqapnKlSRJbTNMS/PLHPtq1vZK4GzgBcAFwG8mOeMh31S1paomqmpibGxs6SuVJEl94ZxpaX6TwKld2+PA/jna3FNV9wH3JbkZOAu4s50SJUlSPzkyLc1vB3B6krVJVgEbgW2z2nwS+NkkK5M8EngWcHvLdUqSpD5xZFqaR1VNJ7kUuBFYAVxTVbuTXNI5vrmqbk9yA3Ar8CDw3qr6av+qliRJbTJMSwuoqu3A9ln7Ns/avhK4ss26JEnSYHCahyRJktSQYVqSJElqyDAtSZIkNWSYliRJkhoyTEuSJEkNGaYlSZKkhgzTkiRpICRZn+SOJHuSXD7H8fOSfDfJLZ2vt/ajTqmb60xLkqS+S7ICuBo4H5gEdiTZVlW3zWr6uar6xdYLlObhyLQkSRoE5wJ7qmpvVR0EtgIb+lyTtCjDtCRJGgSrgX1d25OdfbM9J8lXklyf5BlznSjJpiQ7k+ycmppajlqlIwzTkiRpEGSOfTVr+8vAk6rqLODdwHVznaiqtlTVRFVNjI2NLXGZ0o8yTEuSpEEwCZzatT0O7O9uUFX3VtX3O6+3A8clOaW9EqWHMkxLkqRBsAM4PcnaJKuAjcC27gZJnpAkndfnMpNjDrReqdTF1TwkSVLfVdV0kkuBG4EVwDVVtTvJJZ3jm4GXAb+SZBq4H9hYVbOngkitMkxLkqSB0Jm6sX3Wvs1dr68Crmq7LmkhTvOQJEmSGjJMS5IkSQ0ZpiVJkqSGDNOSJElSQ4ZpSZIkqSHDtCRJktSQYVqSJElqyDAtSZIkNWSYliRJkhoyTEuSJEkNGaYlSZKkhloJ00nWJ7kjyZ4kl8/T5rwktyTZneSmNuqSpFHUy2dup905SQ4leVmb9UnSKFm53D8gyQrgauB8YBLYkWRbVd3W1eaxwHuA9VV1V5LHL3ddkjSKevnM7Wp3BXBj+1VK0uhoY2T6XGBPVe2tqoPAVmDDrDavAD5eVXcBVNXdLdQlSaOol89cgF8FPgb4eStJx2DZR6aB1cC+ru1J4Fmz2pwBHJfks8CJwB9U1ftnnyjJJmATwJo1a5alWEkacot+5iZZDbwY+PfAOQudrJfP3e99b1fzaofMiSee3e8SJA2YNkamM8e+mrW9EjgbeAFwAfCbSc54yDdVbamqiaqaGBsbW/pKJWn49fKZ+y7gsqo6tNjJ/NyVpIW1MTI9CZzatT0O7J+jzT1VdR9wX5KbgbOAO1uoT5JGSS+fuRPA1iQApwDPTzJdVde1U6IkjY42RqZ3AKcnWZtkFbAR2DarzSeBn02yMskjmfmV5O0t1CZJo2bRz9yqWltVp1XVacBHgTcYpCWpmWUfma6q6SSXMnPH+ArgmqraneSSzvHNVXV7khuAW4EHgfdW1VeXuzZJGjW9fOb2tUBJGjFtTPOgqrYD22ft2zxr+0rgyjbqkaRR1stnbtf+X26jJkkaVT4BUZIkSWrIMC1JkiQ1ZJiWJEmSGjJMS5IkSQ0ZpiVJkqSGDNOSJElSQ4ZpSZIkqSHDtCRJktSQYVpaQJL1Se5IsifJ5XMcPy/Jd5Pc0vl6az/qlCRJ/dHKExClYZRkBXA1cD4wCexIsq2qbpvV9HNV9YutFyhJkvrOkWlpfucCe6pqb1UdBLYCG/pckyRJGiCGaWl+q4F9XduTnX2zPSfJV5Jcn+QZc50oyaYkO5PsnJqaWo5aJUlSHximpflljn01a/vLwJOq6izg3cB1c52oqrZU1URVTYyNjS1xmZIkqV8M09L8JoFTu7bHgf3dDarq3qr6fuf1duC4JKe0V6IkSeonw7Q0vx3A6UnWJlkFbAS2dTdI8oQk6bw+l5n/pw60XqkkSeoLV/OQ5lFV00kuBW4EVgDXVNXuJJd0jm8GXgb8SpJp4H5gY1XNngoiSZJGlGFaWkBn6sb2Wfs2d72+Criq7bokSdJgcJqHJEmS1JBhWpIkSWrIMC1JkiQ1ZJiWJEmSGjJMS5IkSQ0ZpiVJkqSGDNOSJElSQ4ZpSZIkqSHDtCRJktSQYVqSJElqyDAtSZIkNWSYliRJkhoyTEuSJEkNGaYlSdJASLI+yR1J9iS5fIF25yQ5lORlbdYnzcUwLUmS+i7JCuBq4EJgHXBRknXztLsCuLHdCqW5GaYlSdIgOBfYU1V7q+ogsBXYMEe7XwU+BtzdZnHSfAzTkiRpEKwG9nVtT3b2HZFkNfBiYPNCJ0qyKcnOJDunpqaWvFCpW89hOsl/n2PfiqUtR5IkPUxljn01a/tdwGVVdWihE1XVlqqaqKqJsbGxJStQmsvRjEyvTnLR4Y0kjwf+culLkiRJD0OTwKld2+PA/lltJoCtSf4BeBnwniQvaqc8aW4rj6Lt/wXcmOT/Y+Zfin8MXLYsVUmSpIebHcDpSdYC3wA2Aq/oblBVaw+/TnIt8GdVdV2bRUqzLRqmk7wf+DLw/wJvBD4ETAMvqqo9y1ueJEl6OKiq6SSXMrNKxwrgmqraneSSzvEF50lL/dLLyPSfAGcBr+v89zRm/vX4qiRfraqPLl95kiTp4aKqtgPbZ+2bM0RX1S+3UZO0mEXDdFV9BvjM4e0kK5lZ//Es4NmAYVqSJEkPS0czZxqY+TUMcGvn6wNLXpEkSZI0JFxnWpIkSWrIMC1JkiQ1dDQPbbmil32SJEnSw8XRjEyfP8e+C5eqEEmSJGnY9LLO9K8AbwCenOTWrkMnAp9frsIkSZKkQdfLah4fAq4Hfge4vGv/96rqW8tSlSRJkjQEelln+rvAd4GLkpwEnA4cD5CEqrp5eUuUJEmSBlPP60wnuRh4EzAO3MLMA1v+Fvj3y1OaJEmSNNiO5gbENwHnAP9YVT8P/O/A1LJUJUmSJA2BownTP6yqHwIk+TdV9TXgqctTliRJkjT4juZx4pNJHgtcB3w6ybeB/ctTliRJkjT4eg7TVfXizsvfTvJXwGOAG5alKkmSJGkIHM3I9BFVddNSFyJJkiQNm6OZMy1JkiSpi2FakiRJamjRMJ1kTRuFSJIkScOml5Hp6w6/SPKxZaxFkiRJGiq9hOl0vX7ychUiSZIkDZtewnTN81qSJEl6WOslTJ+V5N4k3wPOPPy683Xvchco9VOS9UnuSLInyeULtDsnyaEkL2uzPmkui/XbJBuS3JrkliQ7k/xMP+qUpFGw6DrTVbXi8Oskj+/su3s5i5IGQZIVwNXA+cAksCPJtqq6bY52VwA3tl+l9KN67LefAbZVVSU5E/gI8LT2q5Wk4dfT0nhJfivJFHA78LUkU0neurylSX13LrCnqvZW1UFgK7Bhjna/CnwM8B+ZGgSL9tuq+n5VHZ62dwJO4ZOkxnpZGu+/AD8DnFtVJ1fV44BnAT/dOSaNqtXAvq7tyc6+I5KsBl4MbF7oREk2dX6dvnNqamrJC5W6LNpvAZK8OMnXgD8HXjffyey7krSwXkamXwNcVFVfP7yjqvYCr+ock0ZV5tg3ewTvXcBlVXVooRNV1ZaqmqiqibGxsSUrUJpDL/2WqvpEVT0NeBHw9vlOZt+VpIUtOmcaOK6q7pm9s6qmkhy3DDVJg2ISOLVrexzYP6vNBLA1CcApwPOTTFfVdUj90Uu/PaKqbk7y40lOmeuzXpK0sF5Gpg82PCYNux3A6UnWJlkFbAS2dTeoqrVVdVpVnQZ8FHiDQVp9tmi/TfKUdP4FmOQngVXAgdYrlaQR0MvI9FmdJfAO/+rw8K8LAxy/LFVJA6CqppNcyswqHSuAa6pqd5JLOscXnCct9UOP/falwGuSPADcD7y864ZESTRwPA4AABCrSURBVNJROKql8aSHm6raDmyftW/OEF1Vv9xGTdJiFuu3VXUFM8s5SpKO0aJhOsnxwCXAU4BbmRnlmF7uwiRJkqRB18uc6T9h5iarvwOeD/z+slYkSZIkDYle5kyvq6r/DSDJ+4AvLW9JkiRJ0nDoZWT6gcMvnN4hSZIk/aujWc0DZlbw+LGu1T2qqh69bNVJkiRJA8zVPCRJkqSGepnmIUmSJGkOhmlJkiSpIcO0JEmS1JBhWpIkSWrIMC1JkiQ1ZJiWJEmSGjJMS5IkSQ0ZpiVJkqSGWgnTSdYnuSPJniSXL9DunCSHkrysjbokSZKkY7HsYTrJCuBq4EJgHXBRknXztLsCuHG5a5IkSZKWQhsj0+cCe6pqb1UdBLYCG+Zo96vAx4C7W6hJkiRJOmZthOnVwL6u7cnOviOSrAZeDGxe6ERJNiXZmWTn1NTUkhcqSZIkHY02wnTm2Feztt8FXFZVhxY6UVVtqaqJqpoYGxtbsgIlSZKkJla28DMmgVO7tseB/bPaTABbkwCcAjw/yXRVXddCfZIkSVIjbYxM7wBOT7I2ySpgI7Ctu0FVra2q06rqNOCjwBsM0pIkPbwstvpXkg1Jbk1yS2fa58/0o06p27KPTFfVdJJLmVmlYwVwTVXtTnJJ5/iC86QlSdLo61r963xmfqu9I8m2qrqtq9lngG1VVUnOBD4CPK39aqV/1cY0D6pqO7B91r45Q3RV/XIbNUmSpIFyZPUvgCSHV/86Eqar6vtd7U/gofdgSa1rJUxLkiQtYq7Vv541u1GSFwO/AzweeMFcJ0qyCdgEsGbNmnl/4K5dzYsdNmef3e8KRpePE5ckSYOgl9W/qKpPVNXTgBcBb5/rRK7+pTYZpiVJ0iDoZfWvI6rqZuDHk5yy3IVJCzFMS5KkQbDo6l9JnpLOOrpJfhJYBRxovVKpi3OmJUlS3/W4+tdLgdckeQC4H3h5VXkTovrKMC1JkgbCYqt/VdUVwBVt1yUtxGkekiRJUkOGaUmSJKkhw7QkSZLUkGFakiRJasgwLUmSJDVkmJYkSZIaMkxLkiRJDRmmJUmSpIYM05IkSVJDhmlJkiSpIcO0JEmS1JBhWpIkSWrIMC1JkiQ1ZJiWFpBkfZI7kuxJcvkcxzckuTXJLUl2JvmZftQpSZL6Y2W/C5AGVZIVwNXA+cAksCPJtqq6ravZZ4BtVVVJzgQ+Ajyt/WolSVI/ODItze9cYE9V7a2qg8BWYEN3g6r6flVVZ/MEoJAkSQ8bhmlpfquBfV3bk519PyLJi5N8Dfhz4HVznSjJps40kJ1TU1PLUqwkSWqfYVqaX+bY95CR56r6RFU9DXgR8Pa5TlRVW6pqoqomxsbGlrhMSZLUL4ZpaX6TwKld2+PA/vkaV9XNwI8nOWW5C5MkSYPBMC3NbwdwepK1SVYBG4Ft3Q2SPCVJOq9/ElgFHGi9UkmS1Beu5iHNo6qmk1wK3AisAK6pqt1JLukc3wy8FHhNkgeA+4GXd92QKEmSRpxhWlpAVW0Hts/at7nr9RXAFW3XJUmSBoPTPCRJkqSGDNOSJElSQ4ZpSZIkqSHDtCRJktSQYVqSJElqyDAtSZIkNWSYliRJkhoyTEuSJEkNGaYlSZKkhgzTkjRikqxPckeSPUkun+P4K5Pc2vn6fJKz+lGnJI0Cw7QkjZAkK4CrgQuBdcBFSdbNavZ14LlVdSbwdmBLu1VK0ugwTEvSaDkX2FNVe6vqILAV2NDdoKo+X1Xf7mx+ARhvuUZJGhmGaUkaLauBfV3bk51983k9cP18B5NsSrIzyc6pqaklKlGSRodhWpJGS+bYV3M2TH6emTB92Xwnq6otVTVRVRNjY2NLVKIkjY6V/S5AkrSkJoFTu7bHgf2zGyU5E3gvcGFVHWipNkkaOY5MS9Jo2QGcnmRtklXARmBbd4Mka4CPA6+uqjv7UKMkjQxHpiVphFTVdJJLgRuBFcA1VbU7ySWd45uBtwInA+9JAjBdVRP9qlmShplhWpJGTFVtB7bP2re56/XFwMVt1yVJo8hpHpIkSVJDhmlJkiSpIcO0JEmS1JBhWpIkSWrIMC1JkiQ1ZJiWJEmSGjJMS5IkSQ0ZpiVJkqSGDNOSJElSQ4ZpSZIkqSHDtCRJGghJ1ie5I8meJJfPcfyVSW7tfH0+yVn9qFPqZpiWJEl9l2QFcDVwIbAOuCjJulnNvg48t6rOBN4ObGm3SumhDNOSJGkQnAvsqaq9VXUQ2Aps6G5QVZ+vqm93Nr8AjLdco/QQhmlJkjQIVgP7urYnO/vm83rg+rkOJNmUZGeSnVNTU0tYovRQhmlJkjQIMse+mrNh8vPMhOnL5jpeVVuqaqKqJsbGxpawROmhVva7AEmSJGZGok/t2h4H9s9ulORM4L3AhVV1oKXapHk5Mi1JkgbBDuD0JGuTrAI2Atu6GyRZA3wceHVV3dmHGqWHcGRakiT1XVVNJ7kUuBFYAVxTVbuTXNI5vhl4K3Ay8J4kANNVNdGvmiUwTEuSpAFRVduB7bP2be56fTFwcdt1SQtxmockSZLUkGFakiRJasgwLUmSJDVkmJYkSZIaMkxLkiRJDRmmJUmSpIYM09ICkqxPckeSPUkun+P4K5Pc2vn6fJKz+lGnJEnqD8O0NI8kK4CrgQuBdcBFSdbNavZ14LlVdSbwdmBLu1VKkqR+MkxL8zsX2FNVe6vqILAV2NDdoKo+X1Xf7mx+ARhvuUZJktRHPgFRmt9qYF/X9iTwrAXavx64fq4DSTYBmwDWrFmzVPU9LO3av6vfJbTm7Cee3e8SJEmLcGRaml/m2FdzNkx+npkwfdlcx6tqS1VNVNXE2NjYEpYoSZL6yZFpaX6TwKld2+PA/tmNkpwJvBe4sKoOtFSbJEkaAI5MS/PbAZyeZG2SVcBGYFt3gyRrgI8Dr66qO/tQoyRJ6iNHpqV5VNV0kkuBG4EVwDVVtTvJJZ3jm4G3AicD70kCMF1VE/2qWZIktcswLS2gqrYD22ft29z1+mLg4rbrkiRJg8FpHpIkSVJDhmlJkiSpIcO0JEmS1FArYTrJ+iR3JNmT5PI5jr8yya2dr88nOauNuiRJkqRjsexhOskK4GrgQmAdcFGSdbOafR14blWdCbwd2LLcdUmSJEnHqo2R6XOBPVW1t6oOAluBDd0NqurzVfXtzuYXmHk4hiRJkjTQ2gjTq4F9XduTnX3zeT1w/VwHkmxKsjPJzqmpqSUsUZIkSTp6bYTpzLGv5myY/DwzYfqyuY5X1ZaqmqiqibGxsSUsUZIkSTp6bTy0ZRI4tWt7HNg/u1GSM4H3AhdW1YEW6pIkSZKOSRsj0zuA05OsTbIK2Ahs626QZA3wceDVVXVnCzVJkiRJx2zZR6arajrJpcCNwArgmqraneSSzvHNwFuBk4H3JAGYrqqJ5a5NkiRJOhZtTPOgqrYD22ft29z1+mLg4jZqkSRJkpaKT0CUJEmSGjJMS5IkSQ0ZpiVJkqSGDNOSJElSQ4ZpSZIkqSHDtCRJktSQYVqSJElqyDAtSZIkNWSYliRJkhoyTEuSJEkNGaYlSZKkhgzTkiRJUkOGaUmSJKkhw7QkSZLUkGFakkZMkvVJ7kiyJ8nlcxx/WpK/TfIvSX6tHzVK0qhY2e8CJElLJ8kK4GrgfGAS2JFkW1Xd1tXsW8B/Bl7UhxIlaaQ4Mi1Jo+VcYE9V7a2qg8BWYEN3g6q6u6p2AA/0o0BJGiWGaUkaLauBfV3bk519jSTZlGRnkp1TU1PHXJwkjRrDtCSNlsyxr5qerKq2VNVEVU2MjY0dQ1mSNJoM05I0WiaBU7u2x4H9fapFkkaeYVqSRssO4PQka5OsAjYC2/pckySNLFfzkKQRUlXTSS4FbgRWANdU1e4kl3SOb07yBGAn8GjgwSRvBtZV1b19K1yShpRhWpJGTFVtB7bP2re56/U3mZn+IUk6Rk7zkCRJkhoyTEuSpIHg0zs1jJzmIUmS+s6nd2pYOTItSZIGgU/v1FAyTEuSpEGwZE/v9MmdapNhWpIkDYIle3qnT+5UmwzTkiRpEPj0Tg0lw7QkSRoEPr1TQ8kwLS3AZZokqR1VNQ0cfnrn7cBHDj+98/ATPJM8Ickk8F+B30gymeTR/atacmk8aV4u0yRJ7fLpnRpGjkxL83OZJkmStCDDtDQ/l2mSJEkLMkxL83OZJkmStCDDtDQ/l2mSJEkLMkxL83OZJkmStCBX85DmUVXTSQ4v07QCuObwMk2d45uTPAHYCTwaeDDJm4F1VXVv3wqXJEmtMUxLC3CZJkmStBDD9MPVrl39rqA9Z5/d7wokSdKIcs60JEmS1JBhWpIkSWrIMC1JkiQ1ZJiWJEmSGjJMS5IkSQ0ZpiVJkqSGDNOSJElSQ4ZpSZIkqSHDtCRJktSQYVqSJElqyDAtSZIkNWSYliRJkhoyTEuSJEkNGaYlSZKkhgzTkiRJUkOGaUmSJKkhw7QkSZLUkGFakiRJasgwLUmSJDVkmJYkSZIaMkxLkiRJDRmmJUmSpIYM05IkSVJDhmlJkiSpIcO0JEmS1JBhWpIkSWrIMC1JkiQ1ZJiWJEmSGjJMS5IkSQ0ZpiVJkqSGDNOSJElSQ4ZpSZIkqSHDtCRJktSQYVqSJElqyDAtSZIkNWSYliRJkhoyTEuSJEkNGaYlSZKkhgzTkiRJUkOGaUmSJKkhw7QkSZLUkGFakiRJaqiVMJ1kfZI7kuxJcvkcx5PkDzvHb03yk23UJS3GvqthZL/VsLLvahgte5hOsgK4GrgQWAdclGTdrGYXAqd3vjYBf7TcdUmLse9qGNlvNazsuxpWbYxMnwvsqaq9VXUQ2ApsmNVmA/D+mvEF4LFJ/l0LtUkLse9qGNlvNazsuxpKK1v4GauBfV3bk8CzemizGvin7kZJNjHzL1GA7ye5Y2lLPSanAPf0u4ghMGjX6UkLHLPv6rBBu0at9Fuw746AQbtGfuYO3p/JoBq06zRv320jTGeOfdWgDVW1BdiyFEUttSQ7q2qi33UMuiG7TvZdAUN3jZas34J9d9gN2TXyM1dHDNN1amOaxyRwatf2OLC/QRupbfZdDSP7rYaVfVdDqY0wvQM4PcnaJKuAjcC2WW22Aa/p3KX7bOC7VfWQXzdKLbPvahjZbzWs7LsaSss+zaOqppNcCtwIrACuqardSS7pHN8MbAeeD+wBfgC8drnrWgYD+eukATQ018m+qy5Dc40eRv0WhujPpY+G5ho9jPru0PyZ9NnQXKdUzTlNTpIkSdIifAKiJEmS1JBhWpIkSWrIML0EFnv8qSDJNUnuTvLVfteiGfbbxdlvB5N9d3H23cFk313cMPZdw/Qx6vHxp4JrgfX9LkIz7Lc9uxb77UCx7/bsWuy7A8W+27NrGbK+a5g+dr08/vRhr6puBr7V7zp0hP22B/bbgWTf7YF9dyDZd3swjH3XMH3s5nu0qTTI7LcaVvZdDSv77ogyTB+7nh/LKw0Q+62GlX1Xw8q+O6IM08fOR5tqGNlvNazsuxpW9t0RZZg+dr08/lQaNPZbDSv7roaVfXdEGaaPUVVNA4cff3o78JGq2t3fqgZPkg8Dfws8Nclkktf3u6aHM/ttb+y3g8e+2xv77uCx7/ZmGPuujxOXJEmSGnJkWpIkSWrIMC1JkiQ1ZJiWJEmSGjJMS5IkSQ0ZpiVJkqSGDNOSJElSQ4ZpSZIkqaH/H6Yf3o58waCaAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plotting the probability mass function for the Bernoulli distribution\n", "a = np.arange(2) # domain of the bernoulli variable\n", "\n", "colors = ['r','g','y','b']\n", "plt.figure(figsize=(12,8))\n", "for i, theta in enumerate([0.1, 0.2, 0.6, 0.7]):\n", " ax = plt.subplot(1, 4, i+1)\n", " plt.bar(a, bernoulli.pmf(a, theta), label=theta, color=colors[i], alpha=0.2)\n", " ax.xaxis.set_ticks(a)\n", "\n", " plt.legend(loc=0)\n", " if i == 0:\n", " plt.ylabel(\"PDF at $k$\")\n", " \n", "\n", "plt.suptitle(\"Bernoulli probability\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Binomial distribution\n", "Another popular distribution for a discrete random variable is the binomial distribution. A binomial distribution has two parameters $n$ and $\\theta$, where $0 \\le \\theta \\le 1$. The sample generated by a binomial distribution denotes the number of successes observed in a sequence of $n$ binary trials (e.g., toss of a coin) when the probability of each success is $\\theta$. \n", "\n", "The samples that are drawn from a binomial distribution range between 0 and $n$.\n", "\n", "The probability distribution is defined as:\n", "\\begin{equation}\n", "p(k;n,\\theta) = P(X = k) = \\binom{n}{k}\\theta^k (1 - \\theta)^{n-k}\n", "\\end{equation}\n" ] }, { "cell_type": "code", "execution_count": 213, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "20\n" ] } ], "source": [ "#sampling from a binomial distribution\n", "sample = binom.rvs(20,0.9,1)\n", "print(sample)" ] }, { "cell_type": "code", "execution_count": 214, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 33.0, '$k$')" ] }, "execution_count": 214, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#plotting the pmf for a bernoulli distribution\n", "plt.figure(figsize=(12,6))\n", "k = np.arange(0, 22)\n", "for p, color in zip([0.1, 0.3, 0.6, 0.8], colors):\n", " rv = binom(20, p)\n", " plt.plot(k, rv.pmf(k), lw=2, color=color, label=p)\n", " plt.fill_between(k, rv.pmf(k), color=color, alpha=0.3)\n", "plt.legend()\n", "plt.title(\"Binomial distribution\")\n", "plt.tight_layout()\n", "plt.ylabel(\"PDF at $k$\")\n", "plt.xlabel(\"$k$\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Multinoulli distribution\n", "A multinoulli distribution is a generalization of Bernoulli distribution for trials which can take more than two possibilities ($k > 2$). The parameter for multinoulli distribution is a vector ${\\bf \\theta}$ which has $k$ entries. Each entry $\\theta_i$ indicates the probability of observing the category $i$ in a single trial." ] }, { "cell_type": "code", "execution_count": 216, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.16666666666666666,\n", " 0.16666666666666666,\n", " 0.16666666666666666,\n", " 0.16666666666666666,\n", " 0.16666666666666666,\n", " 0.16666666666666666]" ] }, "execution_count": 216, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[1/6.]*6" ] }, { "cell_type": "code", "execution_count": 215, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0, 0, 0, 0, 0, 1]])" ] }, "execution_count": 215, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# generate samples from a multinoulli distribution. Essentially simulated a single roll of dice. Note that the output is a vector of length $k = 6$\n", "np.random.multinomial(1, [1/6.]*6, size=1)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Multinomial distribution\n", "A multinomial distribution is a generalization of Binomial distribution for trials which can take more than two possibilities. The parameters for the multinomial distribution is a vector ${\\bf \\theta}$ and $n$.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4, 4, 4, 2, 4, 2]])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# generate samples from a multinomial distribution. Note that the output is a vector of length $k = 6$\n", "np.random.multinomial(20, [1/6.]*6, size=1)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Poisson distribution\n", "Typically used to model counts. Domain ($\\chi$) is $0 ... \\infty$. It has one parameter, $\\lambda$.\n", "\n", "The *probability mass function* is given as:\n", "$P(X = k) = \\frac{\\lambda^ke^{-\\lambda}}{k!}$.\n", "\n", "The expected value or mean of $X$ is $\\lambda$." ] }, { "cell_type": "code", "execution_count": 219, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0, 100)" ] }, "execution_count": 219, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "lambd = 50\n", "rv = poisson(lambd)\n", "# calculate the pmf for different values of k and plot\n", "k = np.arange(100)\n", "plt.bar(k,rv.pmf(k))\n", "plt.xlim([0,100])" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0, 100)" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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whnNB71LRTUme335f3kTvb23jOBcXLXXsM8DeJM9Lso3e/6r5l2X3VlUj86B3+4tvAf8OfGTY9azzsb+e3indY8Cj7XEr8FJ6nx74dnt+ybBrXed5+R3gi215LOcC+E1gtv1sfAF48RjPxZ8C3wSOA38LPG9c5gL4HL2/nTxL7wzgfc917MBH2nvpSWB3l9fw1hWSJGC0LhlJkobIQJAkAQaCJKkxECRJgIEgSWoMBEkSYCBIkpr/BQxOVxkQOaA+AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# generating samples from this distribution\n", "samples = rv.rvs(1000)\n", "h = plt.hist(samples,bins=20,density=True)\n", "plt.xlim([0,100])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Continuous random variables\n", "A continuous random variable can take an infinite number of possible values. Several interesting distributions exist:\n", "- alpha An alpha continuous random variable.\n", "- beta A beta continuous random variable.\n", "- gamma A gamma continuous random variable.\n", "- expon An exponential continuous random variable.\n", "- gauss Gaussian random variable\n", "\n", "#### Gaussian distribution\n", "One of the most popular distribution is the Gaussian distribution. This distribution is defined for any number of variables. For a single variable case, the distribution is defined using two parameters: $\\mu$ and $\\sigma$. $\\mu$ or the mean can take any value and $\\sigma$ or the standard deviation is $\\ge 0$.\n", "\n", "For a continuous distribution, you cannot compute the probability mass at any value of the random variable. Instead, you can compute the density using the probability density function:\n", "$$p(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}}\\exp[-\\frac{1}{2}(\\frac{x - \\mu}{\\sigma})^2]$$\n", "The random variable represented using a Gaussian distribution can take any value from $-\\infty$ to $\\infty$." ] }, { "cell_type": "code", "execution_count": 230, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 230, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set the parameters\n", "mu = 125\n", "sigma = 8\n", "# draw 1000 samples from this distribution\n", "#samples = norm(mu, sigma).rvs(1000)\n", "# plot an empirical distribution, i.e., a histogram\n", "#h = plt.hist(samples, 30, density=True, alpha=.3)\n", "\n", "# Compute the density at several instances of the random variable\n", "x = np.linspace(90, 170, 10001)\n", "# plot the density\n", "plt.plot(x, norm(mu, sigma).pdf(x), linewidth=2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Real-world example\n", "Consider heights and weights of a population sample" ] }, { "cell_type": "code", "execution_count": 227, "metadata": {}, "outputs": [], "source": [ "hw = pd.read_csv('../data/heightweight.csv')" ] }, { "cell_type": "code", "execution_count": 228, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'Weight (lbs)')" ] }, "execution_count": 228, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = plt.subplot(111)\n", "hw['Weight'].hist(bins=20,ax=ax)\n", "ax.set_xlabel('Weight (lbs)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Multi-dimensional or multivariate Gaussian distribution\n", "A distribution can be defined for multivariate random variables. One example is the multivariate Gaussian. In general, the random variable is a $D$ length vector ${\\bf X}$. The two parameters of this distribution are a mean vector ${\\bf \\mu}$ and a covariance matrix $\\Sigma$. The pdf at any value of ${\\bf X}$ is given by:\n", "$$\n", " \\mathcal{N}({\\bf X}| {\\bf \\mu,\\Sigma}) \\triangleq \\frac{1}{(2\\pi)^{D/2}|{\\bf \\Sigma}|^{D/2}}exp\\left[-\\frac{1}{2}{\\bf (x-\\mu)^\\top\\Sigma^{-1}(x-\\mu)}\\right]\n", "$$\n", "Note that if $D = 1$, it reduces to a univariate Gaussian distribution." ] }, { "cell_type": "code", "execution_count": 233, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#define the parameters for D = 2\n", "mu = np.array([10,10])\n", "Sigma = np.array([[4,1.],[1.,1]])\n", "rv = np.random.multivariate_normal(mu,Sigma)\n", "#sample some points\n", "s = np.random.multivariate_normal(mu,Sigma,1000)\n", "\n", "fig = plt.figure()\n", "plt.subplot(111)\n", "plt.scatter(s[:,0],s[:,1])\n", "\n", "# add a contour plot\n", "smin = np.min(s,axis=0)\n", "smax = np.max(s,axis=0)\n", "t1=np.linspace(smin[0],smax[0],1000)\n", "t2=np.linspace(smin[1],smax[1],1000)\n", "\n", "# evaluate pdf at each of these mesh points\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 9.89485661e-01, -1.43077154e-02],\n", " [ -1.43077154e-02, 9.97270669e+01]])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.cov(s.transpose())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 1 }